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The probability of a seed germinating is $0.6$. a gardener plants $2$ seeds in each of $4$ pots . Find the probability that exactly one seed germinates in each pot.

My attempt $X \sim B(2,.6)$ for one pot and $P(X=1)= .48$. So for the probability that exactly one seed germinates in pot 1 and pot 2 and pot 3 and pot 4, the probability is $(.48)^4$?

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  • $\begingroup$ I added the self-study tag and edited the math notations to use LaTeX formatting (see stats.stackexchange.com/editing-help#latex) $\endgroup$
    – Juho Kokkala
    Commented May 4, 2018 at 5:47
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    $\begingroup$ That is correct - and $0.48^4 = 0.05308416$ if you want to go that last step. $\endgroup$
    – Ben
    Commented May 4, 2018 at 6:05

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You correctly noticed that the distribution for the number of seed germinating, with $n=2$ seeds in a pot and $p=0.6$ probability of germinating, follows a binomial distribution. What follows, you correctly calculated that the probability of exactly one seed in a pot germinating is $0.48$ (from the pmf of the binomial distribution).

Next, you need to realize that the pots are independent (as the description does not say anything that contradicts this) and the conditions are identical (same $p$ for each pot), so we are talking about independent and identically distributed random variables following the binomial distribution parameterized by $n,p$ in each case. Next, you correctly noticed that joint probability of independent random variables is a product of their marginal probabilities, as in your answer.

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