26. A die is thrown, find the probability of following events:

(i) A prime number will appear,

(ii) A number greater than or equal to 3 will appear,

(iii) A number less than or equal to one will appear,

(iv) A number more than 6 will appear,

(v) A number less than 6 will appear.

<p><strong>26.&nbsp;</strong>The sample space of throwing s dice is</p><p>S = {1, 2, 3, 4, 5, 6}, n (S) = 6.</p><p><strong> (i)</strong> Let A be event such that a prime number will appear. Then, </p><p>A = {2, 3, 5}</p><p>? n (A) = 3</p><p>Here; P (A) =&nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mi>n</mi><mrow><mo> (A</mo><mrow></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mrow><mo> (S</mo><mrow></mrow><mo>)</mo></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span></p><p><strong> (ii) </strong>Let B be event such that a number greater than or equal to 3 will appear. Then</p><p>B = {3, 4, 5, 6}</p><p>So, n (B) = 4</p><p>Therefore P (B) =&nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mi>n</mi><mrow><mo> (B</mo><mrow></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mrow><mo> (S</mo><mrow></mrow><mo>)</mo></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></math></span></p><p><strong> (iii)</strong> Let C be event such that a number less than or equal to one will appear. Then, </p><p>C = {1}</p><p>So, n (C) = 1</p><p>? P (C) =&nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mi>n</mi><mrow><mo> (C</mo><mrow></mrow><mo>)</mo></mrow></mrow><mrow><mi>n</mi><mrow><mo> (S</mo><mrow></mrow><mo>)</mo></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mrow></math></span></p><p><strong> (iv)</strong> Let D be event such that a number more than 6 appears. Then, </p><p>D =∅</p><p>So, n (D) = 0</p><p>? P (D) =&nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mi>n</mi><mrow><mo> (</mo><mrow></mrow><mo>D)</mo></mrow></mrow><mrow><mi>n</mi><mrow><mo> (</mo><mrow></mrow><mo>S)</mo></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>0</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>=</mo><mn>0</mn></mrow></math></span></p><p><strong> (v)</strong> Let E be event such that a number less than 6 appears. Then</p><p>E = {1, 2, 3, 4, 5}</p><p>So, n (E) = 5</p><p>? P (E) =&nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mi>n</mi><mrow><mo> (</mo><mrow></mrow><mo>E)</mo></mrow></mrow><mrow><mi>n</mi><mrow><mo> (</mo><mrow></mrow><mo>S</mo></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mrow></math></span></p>

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