Question

For a particular type of plant 30% have blue flowers. A garden center sells these plants in trays of 15 plant mixed colours. A tray is selected at random (6 Marks) Please give your answer correct to three decimal places (e.g. 0.123) Find the probability that the number of plants with blue flowers in this tray is: a) (exactly 5) b) (at least 2)

Answer 1

n = 15, p = 0.3

X : Random variable for blue flower in the tray

X follows a binomial distribution with n = 15 and p = 0.3

Binomial Probability is calculated as

n-1 P(X = x) = C*p" 1-p)"

a)

We need to find P(X =5)

$\small P(X =5) = _{5}^{15}\textrm{C} * 0.3^{5} * (1-0.3)^{15-5}$$\small P(X =5) = _{5}^{15}\textrm{C} * 0.3^{5} * (1-0.3)^{15-5} = 0.206$

So, the answer is 0.206

b).

P( at least 2) = P(X >=2 ) = 1 - P(X <2)

= 1 - [P(X =0) + P(X =1) ]

= 1 - [ 0.00474756151 + 0.03052003828 ]

= 1 - 0.0352646

=  0.965

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