Question

10.If a seed is planted, it has a 80% chance of growing into a healthy plant. If 9 seeds are planted, what is the probability that exactly 2 don't grow?

Answer 1

SOLUTION :

GIVEN

• A seed is planted, it has a 80% chance of growing into a healthy plant

• 9 seeds are planted

TO DETERMINE

The probability that exactly 2 don't grow i.e

$\sf{P(X=2)}$

FORMULA TO BE IMPLEMENTED

If a trial is repeated n times and p is the probability of a success and q that of failure then the probability of r successes is

$\displaystyle \sf{ \sf{P(X=r) = \: \: }\large{ {}^{n} C_r}\: {p}^{r} \: \: {q}^{n - r} } \: \: \: \: \: where \: q \: = 1 - p$

EVALUATION

Here if a seed is planted, it has a 80% chance of growing into a healthy plant

So it has a (100% - 80%) = 20% chance of growing into a healthy plant

Let p be the probability of not growing a seed into a healthy plant

Then

$\displaystyle \sf{}p = \frac{20}{100} = \frac{1}{5}$

$\therefore \: \displaystyle \sf{}q= 1 - \frac{1}{5} = \frac{4}{5}$

Hence the required probability

= $\sf{P(X=2)}$

$\displaystyle \sf{ = }\large{ {}^{9} C_2}\: { \bigg( \frac{1}{5} \bigg)}^{2} \: \: { \bigg( \frac{4}{5} \bigg)}^{9 - 2}$

$\displaystyle \sf{ = } \frac{9 \times 8}{2} \times { \bigg( \frac{1}{5} \bigg)}^{2} \times { \bigg( \frac{4}{5} \bigg)}^{7}$

$\sf{} = 36 \times 0.008$

$\sf{} = 0.288$

FINAL RESULT

Hence the probability that exactly 2 seed don't grow is 0.288

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LEARN MORE FROM BRAINLY

In a binomial distribution , p=1/2,q=1/2, n =6.

Then p(x=2)

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