<span>P(black socks): 24/42 or 12/21
P(black socks without replacement): 23/41. Consequently, the chance of randomly selecting 2 black socks, without replacement, from the basket is 12/21×23/41=276/861, equivalent to 32%. Hope this helps!</span>
x:200
x/200 =.2121212121...
200(x/200) = 200(.2121212121...)
x = 42.4242...
The expectation is that a player would achieve 42 hits over 200 at-bats.
a) The price of one medium drink is $3.80. b) The price of a large popcorn is $6.25. To solve, let the cost of a medium drink be $x and a large popcorn be $y. A couple spent $13.85 on 2 medium drinks and a large popcorn. Thus, 2x + y = 13.85. A family spent $23.90 on 3 medium drinks and 2 large popcorns; hence, 3x + 2y = 23.90. Using the elimination method, we multiply the first equation by 2, leading to 4x + 2y = 27.70. Now, subtract the second equation from this new equation, which simplifies to 4x - 3x = 3.80, giving us x = 3.80. Substituting x back into the first equation yields 2(3.80) + y = 13.85, resulting in y = 6.25. Therefore, the cost of one medium drink is $3.80 and a large popcorn is $6.25.
