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Fifteen coupons are numbered 1, 2, 3, ....., 15 respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupons is at most 9, is :
- a)(1/15)7
- b)(3/7)7
- c)(8/15)7
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Fifteen coupons are numbered 1, 2, 3, ....., 15 respectively. Seven co...
Total coupons = 15
1 < selected coupon number < 9
i.e., 1, 2, 3, 4, 5, 6,, 7, 8, 9
1 < selected coupon number < 9
i.e., 1, 2, 3, 4, 5, 6,, 7, 8, 9
∴ Probability of one selected coupon to have number 
Hence, the required probability
= (3/5) x (3/5) x ....... 7 times = (3/5)7 (Using multiplicative principle for independent events)
Hence, the required probability
= (3/5) x (3/5) x ....... 7 times = (3/5)7 (Using multiplicative principle for independent events)
Most Upvoted Answer
Fifteen coupons are numbered 1, 2, 3, ....., 15 respectively. Seven co...
To solve this problem, we need to find the probability that the largest number appearing on a selected coupon is at most 9. Let's break down the solution into smaller steps:
Step 1: Finding the probability of selecting a coupon with a number less than or equal to 9
Out of the 15 coupons, there are 9 coupons with numbers from 1 to 9. Therefore, the probability of selecting a coupon with a number less than or equal to 9 is 9/15 = 3/5.
Step 2: Finding the probability of selecting a coupon with a number greater than 9
Out of the 15 coupons, there are 6 coupons with numbers from 10 to 15. Therefore, the probability of selecting a coupon with a number greater than 9 is 6/15 = 2/5.
Step 3: Finding the probability of selecting a coupon with a number less than or equal to 9 in all 7 selections
Since the selections are made with replacement, each selection is independent. Therefore, the probability of selecting a coupon with a number less than or equal to 9 in all 7 selections is (3/5)^7.
Step 4: Simplifying the expression
To find the final probability, we simplify the expression (3/5)^7. This can be done by multiplying the numerator and denominator of the fraction by 5^7.
(3/5)^7 = (3^7)/(5^7) = (2187)/(78125) = 3/10925
Therefore, the probability that the largest number appearing on a selected coupon is at most 9 is 3/10925.
The correct answer is option B) (3/7)^7.
Step 1: Finding the probability of selecting a coupon with a number less than or equal to 9
Out of the 15 coupons, there are 9 coupons with numbers from 1 to 9. Therefore, the probability of selecting a coupon with a number less than or equal to 9 is 9/15 = 3/5.
Step 2: Finding the probability of selecting a coupon with a number greater than 9
Out of the 15 coupons, there are 6 coupons with numbers from 10 to 15. Therefore, the probability of selecting a coupon with a number greater than 9 is 6/15 = 2/5.
Step 3: Finding the probability of selecting a coupon with a number less than or equal to 9 in all 7 selections
Since the selections are made with replacement, each selection is independent. Therefore, the probability of selecting a coupon with a number less than or equal to 9 in all 7 selections is (3/5)^7.
Step 4: Simplifying the expression
To find the final probability, we simplify the expression (3/5)^7. This can be done by multiplying the numerator and denominator of the fraction by 5^7.
(3/5)^7 = (3^7)/(5^7) = (2187)/(78125) = 3/10925
Therefore, the probability that the largest number appearing on a selected coupon is at most 9 is 3/10925.
The correct answer is option B) (3/7)^7.
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Fifteen coupons are numbered 1, 2, 3, ....., 15 respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupons is at most 9, is :a)(1/15)7b)(3/7)7c)(8/15)7d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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