Question #154685
The manufacture of fertilizer guarantees that, with the aid of the fertilizer, 75% of planted seeds will germinate. Suppose the manufacturer is correct. If 7 seeds planted with the fertilizer are randomly selected, what is the probability that more than 5 of them germinate? Carry your intermediate computations to the least four decimal places, and round your answer to two decimal places.
Expert's answer
We are to determine the probability that more than 5 of 7 seeds (i.e. 6 or 7) germinate.
The probability that all 7 seeds germinate is equal 0.757= 0.133484 = 13.3484%.
The probability that only the first (only the second, etc) seed does not germinate is equal 0.25 * 0.756= 0.044495 = 4.4495%.
The probability that 6 seeds germinate is the sum of the probabilities that only the first seed does not germinate, only the second one does not germinate, etc, and equals to 7 * 0.044495 = 0.311465 = 31.1465%.
The total probability that more than 5 of 7 seeds germinate is the sum of the probabilities that 7 seeds germinate and that 6 seeds germinate, i.e. 13.3484% + 31.1465% = 44.4949%.
