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five dices are thrown 150 times. The occurrences of an odd face are considered a success .tn how many throws do you expect 1)less than 4 successes 2)at least 3 succeses3)exactly one success |
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Answer» Given : 5 dices are thrown 150 times The occurrences of an odd face are considered a success To Find : how many throws do you expect 1)less than 4 successes 2)at least 3 success 3)EXACTLY one success Solution: dice has 1 to 6 NUMBERS 3 odd 1 , 3 , 5 probability of odd number p = 3/6 = 1/2 q = 1 - 1/2 = 1/2 p(x) = ⁿCₓpˣqⁿ⁻ˣ n = 5 less than 4 successes = 1 - P(4) - P(5) = 1 - ⁵C₄(1/2)⁴(1/2)¹ - ⁵C₁(1/2)⁵(1/2)⁰ = 1 - 5/32 - 1/32 = 26/32 out of 150 = 150 * 26/32 = 121.87 = 122 in 122 throws expected less than 4 successes at least 3 success = P(3) + p(4) + P(5) = ⁵C₃(1/2)³(1/2)² + ⁵C₄(1/2)⁴(1/2)¹ + ⁵C₁(1/2)⁵(1/2)⁰ = 10/32 + 5/32 + 1/32 = 16/32 = 1/2 150 * 1/2 = 75 in 75 throws expected at least 3 success exactly one success = P(1) = ⁵C₁(1/2)¹(1/2)⁴ = 5/32 150 * 5/32 = 23.4 = 23 Learn More: Find the probability distribution of the numbers obtained in throwing ... A sample of four chocolate bars are randomly SELECTED from a box of ... there three urns. the first urn contains 3 green balls and 2 white balls ... |
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