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We are given that we have $9$pizzas in the oven: $3$of the $9$have thick crust and $2$of the $3$thick-crust pizzas have mushrooms. Of the remaining $6$pizzas , $4$have mushrooms . We need to find if the events 鈥渢hick-crust pizza鈥� and 鈥減izza with mushrooms鈥� mutually exclusive .

For events to be mutually exclusive when $(A鈭�B)=0$

The given events are not mutually exclusive because thick crust pizza have common things with mushroom . So the given events are not mutually exclusive .

We are given that we have $9$pizzas in the oven: $3$of the $9$have thick crust and $2$of the $3$thick-crust pizzas have mushrooms. Of the remaining $6$pizzas , $4$ have mushrooms . We are required to find if the events 鈥渢hick-crust pizza鈥� and 鈥減izza with mushrooms鈥� independent .

Let A be thick crust and Let B= mushrooms

$\frac{2}{3}鈮�\frac{4}{7}$

$\frac{1}{2}鈮�\frac{3}{7}$

We are given $9$pizzas and we randomly select $2$of the pizzas in the oven. We need to find the probability that both pizzas have mushroom .

The required probability is P (first pizza to be mushroom one )$脳$P(second mushroom pizza)

Required probability $=\frac{6}{9}脳\frac{5}{8}$

$=$$\frac{5}{12}$