Answer:
The probability that the cell will be killed is 0.9328.
Step-by-step explanation:
We are given that five nanotubules are inserted in a single cancer cell. Independently of each other, they become exposed to near-infrared light with probabilities 0.2, 0.4, 0.3, 0.6, and 0.5.
Let the event that a cell is killed be 'A' and the event where the ith nanotubule kill the cell be '
'.
This means that the cell will get killed if
happens. This represents that the cell is killed if nanotubule 1 kills the cell, or nanotubule 2 kills the cell, and so on.
Here, P(
) = 0.2, P(
) = 0.4, P(
) = 0.3, P(
) = 0.6, P(
) = 0.5.
So, the probability that the cell will be killed is given by;
P(A)= ![1 - [(1 - P(\text{B}_1)) \times (1 - P(\text{B}_2)) \times (1 - P(\text{B}_3)) \times (1 - P(\text{B}_4)) \times (1 - P(\text{B}_5))]](https://tex.z-dn.net/?f=1%20-%20%5B%281%20-%20P%28%5Ctext%7BB%7D_1%29%29%20%5Ctimes%20%281%20-%20P%28%5Ctext%7BB%7D_2%29%29%20%5Ctimes%20%281%20-%20P%28%5Ctext%7BB%7D_3%29%29%20%5Ctimes%20%281%20-%20P%28%5Ctext%7BB%7D_4%29%29%20%5Ctimes%20%281%20-%20P%28%5Ctext%7BB%7D_5%29%29%5D)
P(A) = ![1 - [(1 - 0.2) \times (1 - 0.4) \times (1 - 0.3) \times (1 - 0.6) \times (1 - 0.5)]](https://tex.z-dn.net/?f=1%20-%20%5B%281%20-%200.2%29%20%5Ctimes%20%281%20-%200.4%29%20%5Ctimes%20%281%20-%200.3%29%20%5Ctimes%20%281%20-%200.6%29%20%5Ctimes%20%281%20-%200.5%29%5D)
P(A) = 
P(A) = 1 - 0.0672 = 0.9328
Hence, the probability that the cell will be killed is 0.9328.