Thread: Prob that person A tossed coin once to get H and that the other 1 needed 9 throws

Hey, I have the following question... I know the probabilities for each event happening independently, but not in the way the question is asking. Should I multiply or add the probabilities? What should I do? Cheers!

The problem says that person A tosses a fair coin until it lands heads, and that then person B does the same. In the end, they toss it 10 times. What is the probability that person A only tossed it once?

Well, I have that the probability that person A gets heads with only once throw is 0.5, and that the probability that person gets heads with 9 throws is 9/(2^9)=9/512=0.02

So I don't know if I should add them (which would give P=0.52) or multiply them... or something different. Thanks a lot!

Hello, buenogilabert!

Person tosses a fair coin until it lands heads, then person does the same.
In the end, they toss it 10 times.
What is the probability that person tossed it only once?

tossed once and got a Head,
. . then tossed nine times to grt a Head.

We want: .

. . . . . . . . . . . . . . . .


Therefore: .