Respuesta :
Answer:
A. 11.48%
Step-by-step explanation:
We have been given that there are 182 total seats on the plane, 62 are window seats, 58 are middle seats, and the rest are aisle seats.
Let us find the number of aisle seats.
[tex]\text{Total number of aisle seats}=182-(62+58)[/tex]
[tex]\text{Total number of aisle seats}=182-120[/tex]
[tex]\text{Total number of aisle seats}=62[/tex]
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}[/tex]
[tex]\text{Probability that Harry will get aisle seat}=\frac{\text{Total number of aisle seats}}{\text{Total number of all seats}}[/tex]
[tex]\text{Probability that Harry will get aisle seat}=\frac{62}{182}[/tex]
Since one aisle seat is assigned to Harry, so number of left aisle seats will be 61 and number of total seats left will be 181.
[tex]\text{Probability that Jay will get aisle seat}=\frac{61}{181}[/tex]
Since the probability of both events is dependent, so we will use formula:
[tex]P(\text{A and B})=P(A)*P(B)[/tex]
[tex]P(\text{Both Harry and Jay will get aisle seat})=\frac{62}{182}\times \frac{61}{181}[/tex]
[tex]P(\text{Both Harry and Jay will get aisle seat})=\frac{62\times61}{182\times181}[/tex]
[tex]P(\text{Both Harry and Jay will get aisle seat})=\frac{3782}{32942}[/tex]
[tex]P(\text{Both Harry and Jay will get aisle seat})=0.1148078\approx 0.1148[/tex]
To convert our probability in percentage we will multiply 0.1148 by 100.
[tex]P(\text{Both Harry and Jay will get aisle seat})=0.1148\times 100[/tex]
[tex]P(\text{Both Harry and Jay will get aisle seat})=11.48\%[/tex]
Therefore, the probability that both Harry and Jay will be assigned aisle seats on the same plane, is 11.48% and option A is the correct choice.
