Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

A jar of 150 jelly beans contains 22 red jelly beans, 38 yellow, 20 green, 28 purple, 26 blue, and the rest are orange.Let B = the event of getting a blue jelly beanLet G = the event of getting a green jelly bean.Let O = the event of getting an orange jelly bean.Let P = the event of getting a purple jelly bean.Let R = the event of getting a red jelly bean.Let Y = the event of getting a yellow jelly bean.What is the probability of drawing a red jelly bean in the first draw WITHOUT replacing the red jelly bean, then choosing a blue jelly bean in the second draw?Use 4 decimal places for this problem. Do not round your answers for intermediate steps, only for the final answer.

Sagot :

MrRoyal

Answer:

[tex]P(R\ and\ B) = 0.0256[/tex]

Step-by-step explanation:

Given

[tex]Red = 22[/tex]

[tex]Yellow = 38[/tex]

[tex]Green = 20[/tex]

[tex]Purple = 28[/tex]

[tex]Blue = 26[/tex]

[tex]Orange = 16[/tex]

Required

Determine the probability of red then blue jelly? i.e. P(R and B)

From the question, we understand that the red jelly bean was not replaced. This means that the number of jelly beans reduced by 1 after the picking of the red jelly bean

So, we have:

[tex]P(R\ and\ B) = P(R)\ and\ P(B)[/tex]

This is then solved further as:

[tex]P(R\ and\ B) = P(R)\ *\ P(B)[/tex]

[tex]P(R\ and\ B) = \frac{n(R)}{Total}\ *\frac{n(B)}{Total - 1}[/tex]

The probability has a denominator of Total - 1 because the number of jelly beans reduced by 1 after the picking of the red jelly bean

The equation becomes:

[tex]P(R\ and\ B) = \frac{22}{150}\ *\frac{26}{150- 1}[/tex]

[tex]P(R\ and\ B) = \frac{22}{150}\ *\frac{26}{149}[/tex]

[tex]P(R\ and\ B) = \frac{22*26}{150*149}[/tex]

[tex]P(R\ and\ B) = \frac{572}{22350}[/tex]

[tex]P(R\ and\ B) = 0.02559284116[/tex]

[tex]P(R\ and\ B) = 0.0256[/tex]

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.