A spinner gives either red or blue. The probability of red is $p$. It is spun twice independently.

Question

A spinner gives either red or blue. The probability of red is $p$. It is spun twice independently.
The probability of obtaining exactly one red is $\frac38$.

Show that $2p(1-p)=\frac38$.
Find both possible values of $p$.
Explain why the information does not identify a unique value of $p$.
Given that red is more likely than blue, find the probability of obtaining two reds.

Accepted Answer

(a) $2p(1-p)=\frac38$; (b) $\frac14,\frac34$; (c) Colour-swapping preserves “exactly one red”; (d) $\frac9{16}$

Probability

Probability