Question

Suppose that the probability a seed will germinate is 80%. What is the probability that 7 of these seeds will germinate when 10 are planted? a. 1.0068 b. 25.17 c. 120 d. 0.201

Answer 1

Your answer will be letter B

Answer 2

Answer: d. 0.201

Step-by-step explanation:

Given: The probability a seed will germinate = 80%

i.e. $p= 0.8$

Then probability of a seed will not germinate is given by :-

$q= 1-p$

i.e $q=1-0.8$

i.e. $q=0.2$

By Binomial Distribution, the probability of getting r successes in n trials is given by :-

$P(r)=^nC_r\ p^rq^{n-r}$

Now , the probability that 7 (r=7) of these seeds will germinate when 10 (n=10) are planted is given by :-

$P(7)=^{10}C_7\ (0.8)^7(0.2)^{10-7}\\\\=\dfrac{10!}{(10-7)!7!}(0.8)^7(0.2)^3\\\\=\dfrac{10\times9\times8}{3\times2}(0.8)^7(0.2)^3\\\\=0.201326592\approx0.201$