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31. When three coins are tosses we have the sample space,

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

So, n (S) = 8

(i) Let A: 3 heads occurs.

A = {HHH}

So, n (A) = 1

? P (A) = $\frac{1}{8}$

(ii) Let B: 2 heads occurs

B = {HHT, HTH, THH}

So, n (B) = 3

? P (B) = $\frac{3}{8}$

(iii) Let C: at least 2 heads occurs i.e. 2 heads or more

C = {HHT, HTH, THH, HHH}

So, n (C) = 4

? P (C) = $\frac{4}{8}=\frac{1}{2}$

(iv) Let D: at most 2 heads occurs i.e. 2 heads or less

D = {TTT, HTT, THT, TTH, HHT, HTH, THH}

So, n (D) = 7

? P (D) = $\frac{7}{8}$

(v) Let E: no head occurs

E = {TTT}

So, n (E) = 1

? P (E) = $\frac{1}{8}$

(vi) Let F: 3 tails occurs

F = {TTT}

So, n (F) = 1

? P (F) = $\frac{1}{8}$

(vii) Let G: exactly two tails occurs

G = {TTH, THT, HTT}

So, n (G) = 3

? P (G) = $\frac{3}{8}$ .

(viii) Let H: no tail occurs

H = {HHH}

So, n (H) = 1

? P (H) = $\frac{1}{8}$ .

(ix) Let I: atmost two tails i.e. two tails or less

I = {HHH, THH, HTH, HHT, HTT, THT, TTH}

So, n (I) = 7

? P (I) = $\frac{7}{8}$

30. When a coin is tossed four times we have the sample space,

S = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, THHT, TTHH, THTH, HTHT, HTTH, TTTH, TTHT, THTT, HTTT, TTTT}

So, n (S) = 16.

Case I: When the outcome is all head, the amount is 1 + 1 + 1 + 1 =? 4 gain

Case II: When the outcome is 3 head and one tail, the amount is

1 + 1 + 1 – 1.50 = 3 – 1.50 =? 1.50 gain

Case III: When the outcome is 2 head and 2 tail, the amount is

1 + 1 – 1.50 – 1.50 = 2 – 3 =? 1 lose.

Case IV: When the outcome is 1 head and 3 tail, the amount is

1 – 1.50 – 1.50 – 1.50 = 1 – 4.50 =? 3.50 lose.

Case V: When the outcome is all tail, the amount is

–1.50 – 1.50 – 1.50 – 1.50 = –6 =? 6 lose.

Let A be event such that person wins ?4. Then,

A = {HHHH}

So, n (A) = 1

? P (A) = $\frac{1}{16}$

Let B: person wins ?1.5. Then,

B = {HHHT, HHTH, HTHH, THHH}

So, n (B) = 4

? P (B) = $\frac{4}{16}=\frac{1}{4}$

Let C: person loses ?1. Then,

C = {HHTT, THHT, TTHH, THTH, HTHT, HTTH}

So, n (C) = 6

? P (C) = $\frac{6}{16}=\frac{3}{8}$

Let D: person loses ?3.50. Then,

D = {HTTT, THTT, TTHT, TTTH}

So, n (D) = 4

? P (D) = $\frac{4}{16}=\frac{1}{4}$

Let E: person loses ?6. Then,

E = {TTTT}

So, n (E) = 1

? P (E) = $\frac{1}{16}$ .

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Eligibility Criteria: Candidates must first qualify for the MBA eligibility criteria, i.e., a bachelor's degree in any stream with a minimum of 50% aggregate in their last qualifying examination. 

Application Process: The MBA admission process begins once candidates visit the official website of the university. Students who qualify for the MBA eligibility criteria must fill out the online application form.

Selection Process: Candidates are shortlisted based on the entrance examination scores- CAT/ MAT/ XAT/ JNU CET, etc., etc.—followed by a personal interview and group discussions. 

Final Admission: Once candidates are shortlisted, they are requested for document verification and seat finalisation. Applicants must pay the MBA course fee to secure a seat at JNU Jaipur. 

To apply for an MBA at Jaipur National University, you first need to make sure you meet the eligibility criteria — a bachelor's degree in any stream with at least 50% marks (45% for reserved categories). You can apply using scores from exams like CAT, MAT, CMAT, XAT, or ATMA, or you can take the university's own entrance test if you haven't appeared for any national-level exam. The next step is to fill out the online application form on the JNU website, upload your documents, and pay the application fee. Shortlisted candidates are invited for a Group Discussion and Personal Interview. Your final selection will be based on your exam score, GD and PI performance, and past academic record. Once you get an admission offer, you confirm your seat by paying the fees and submitting your original documents for verification.