probability maybe conditional probability

splitting events

A pitcher throws 60% strikes. A batter does not wing. What is the probability that a batter will get 4 balls before he gets 3 strikes. In other words, what is the probability of getting a base on balls when a batter doesn't swing and a pitcher throws 60% strikes. Thank you:

Splitting Events
In our baseball game, the only statistics available say that 60% of pitches are strikes and from this I can say that 40% of pitches are balls. I also know that a batter has a 50% chance of batting right handed and a 50% chance of batting left handed. How can I combine these to get probability I want?
Call y the event that the selected batter is right handed. The event I'm really wanting is x, that this batter will walk first. I split this into two smaller events: x&y and x&not y. These two events are mutually exclusive(both can't occur at the same time). So, P(x)=P(x&y)+P(x&not y). Expressing P(x&y) in terms of conditional probability, I get P(x&y)=P(x|y)P(y) and similarly
P(x&not y)=P(x|not y)P(not y). Put these into the conditional probability formula P(x|y)=P(x&y)/P(y).
I get P(x)=P(x|y)P(y)+P(x|not y)P(not y). At this point I can use the data I have(x|y)=40%(50%)+60%(50%)
= .2+.3=.5=50%.
Thus, the probability of getting a base on balls when a batter doesn't swing and a pitcher throws 60% strikes is 50%.

afrazer721 said:

A pitcher throws 60% strikes. A batter does not wing. What is the probability that a batter will get 4 balls before he gets 3 strikes. In other words, what is the probability of getting a base on balls when a batter doesn't swing and a pticher throws 60% strikes. Thank you:
I think this is an conditional probability problem. Is this the correct answer to the probabilty problem?:

Click to expand...

You have three cases to consider.

1. The probability that there are four balls in a row.
2. The probability that the fifth pitch is the fourth ball.
3. The probability that the sixth pitch is the fourth ball.