Math  /  Data & Statistics

QuestionMore pitching: A baseball pitcher threw 3935 pitches during part of a recent season. Of these, 1947 were thrown with no strikes on the batter, 996 were thrown with one strike, and 992 were thrown with two strikes.
Part 1 of 2 (a) What is the probability that a baseball pitch is thrown with no strikes? Round your answer to four decimal places. P(P( A baseball pitch thrown with no strikes )=0.4948)=0.4948
Part: 1/21 / 2
Part 2 of 2 (b) What is the probability that a baseball pitch is thrown with fewer than two strikes? Round your answer to four decimal places. P(AP(A baseball pitch thrown with fewer than two strikes )=)= \square Skip Part Chack

Studdy Solution

STEP 1

What is this asking? Out of all the pitches a baseball pitcher threw, what are the chances a pitch was thrown with no strikes, and what are the chances a pitch was thrown with *less* than two strikes? Watch out! Don't mix up "less than" with "less than or equal to"!
Also, make sure to round correctly at the end.

STEP 2

1. Calculate the no-strike probability.
2. Calculate the fewer-than-two-strikes probability.

STEP 3

We're given that the pitcher threw a **total** of 39353935 pitches.
This is our **total number of events**.
Out of these, 19471947 pitches were thrown with no strikes.
This will be our **favorable outcome** for the no-strike scenario.

STEP 4

**Probability** is calculated as the number of **favorable outcomes** divided by the **total number of possible outcomes**.
So, the probability of a pitch with no strikes is:
Number of pitches with no strikesTotal number of pitches=19473935\frac{\text{Number of pitches with no strikes}}{\text{Total number of pitches}} = \frac{1947}{3935}

STEP 5

Now, let's **calculate the result**:
194739350.49479034307\frac{1947}{3935} \approx 0.49479034307

STEP 6

We need to round our answer to four decimal places.
The fifth decimal place is a 99, which is greater than or equal to 55, so we round up the fourth decimal place.
This gives us a **final probability** of 0.49480.4948.

STEP 7

"Fewer than two strikes" means either **zero strikes or one strike**.
We know there were 19471947 pitches with no strikes and 996996 pitches with one strike.
To find the **total number of favorable outcomes**, we add these together:
1947+996=29431947 + 996 = 2943

STEP 8

The **total number of pitches** remains the same at 39353935.
So, the probability of a pitch with fewer than two strikes is:
Number of pitches with fewer than two strikesTotal number of pitches=29433935\frac{\text{Number of pitches with fewer than two strikes}}{\text{Total number of pitches}} = \frac{2943}{3935}

STEP 9

Let's **calculate the result**:
294339350.74787801778\frac{2943}{3935} \approx 0.74787801778

STEP 10

Rounding to four decimal places, we look at the fifth decimal place, which is an 88.
Since 88 is greater than or equal to 55, we round up the fourth decimal place.
This gives us a **final probability** of 0.74790.7479.

STEP 11

(a) The probability a pitch is thrown with no strikes is 0.49480.4948. (b) The probability a pitch is thrown with fewer than two strikes is 0.74790.7479.

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