Question

star233 · Accepted Answer

To solve this problem, we need to use the concept of joint probability. Let

P (L)

be the probability that a senior is left-handed,

P (W)

be the probability that a senior prefers writing by hand, and

P (T)

be the probability that a senior prefers typing. We can use the information in the table to calculate these probabilities:

P (W) = \frac{21}{45} = \frac{7}{15}

P (T) = \frac{24}{45} = \frac{8}{15}

P (R) = \frac{23}{44}

P (L) = \frac{21}{44}

where

R

denotes right-handedness.
Now we can use the joint probability formula to calculate the probability that a senior is both left-handed and prefers writing by hand:

P (L \cap W) = P (L) \cdot P (W) = \frac{7}{15} \cdot \frac{21}{44} = \frac{49}{220}

To find out how many seniors are expected to be left-handed, we can use the following formula:

E = N \cdot P (L) = 176 \cdot \frac{21}{44} \approx 84

Therefore, we would expect approximately 84 seniors out of a sample of 176 to be left-handed based on the information in the tables.

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