at a schools open house, t - shirts and sweatshirts were sold. each item was purchased by either a student…

at a schools open house, t - shirts and sweatshirts were sold. each item was purchased by either a student or a parent. the two - way frequency table summarizes a random sample of 70 items sold that night.\n| | student | parent |\n|--|--|--|\n| t - shirt | 18 | 21 |\n| sweatshirt | 17 | 14 |\nlet t - shirt be the event that an item randomly chosen from among those sold was a t - shirt. let parent be the event that an item randomly chosen from among those sold was purchased by a parent. find the following probabilities. write your answers as decimals.\n(a) p(parent) =\n(b) p(t - shirt and parent) =\n(c) p(t - shirt | parent) =

at a schools open house, t - shirts and sweatshirts were sold. each item was purchased by either a student or a parent. the two - way frequency table summarizes a random sample of 70 items sold that night.\n| | student | parent |\n|--|--|--|\n| t - shirt | 18 | 21 |\n| sweatshirt | 17 | 14 |\nlet t - shirt be the event that an item randomly chosen from among those sold was a t - shirt. let parent be the event that an item randomly chosen from among those sold was purchased by a parent. find the following probabilities. write your answers as decimals.\n(a) p(parent) =\n(b) p(t - shirt and parent) =\n(c) p(t - shirt | parent) =

Answer

Explanation:

Step1: Calculate P(parent)

The number of items purchased by parents is (21 + 14=35). The total number of items sold is (70). So (P(\text{parent})=\frac{35}{70}=0.5).

Step2: Calculate P(T - shirt and parent)

The number of T - shirts purchased by parents is (21). The total number of items sold is (70). So (P(\text{T - shirt and parent})=\frac{21}{70}=0.3).

Step3: Calculate P(T - shirt | parent)

By the formula for conditional probability (P(A|B)=\frac{P(A\cap B)}{P(B)}). Here (A) is the event of a T - shirt and (B) is the event of a parent. We know (P(\text{T - shirt and parent}) = 0.3) and (P(\text{parent})=0.5). So (P(\text{T - shirt}|\text{parent})=\frac{0.3}{0.5}=0.6).

Answer:

(a) (0.5) (b) (0.3) (c) (0.6)