Iron Dome intercepts a drone. Photo source: Defense News
Iran promises to reply to Israel’s bombing of its embassy in Damascus last week. The news media speculated that Tehran would hit the Israelis before Ramadan ended. This is partly because Muslims are most likely to support Iran, which is Shi’a, during this religious period of sacrifice and reflection. After all, they may be prone to consider Israel’s alleged sins in attacking in what was technically Iranian soil dedicated to diplomacy. (The embassy had sheltered the Iranian general directing operations of the Islamic Revolutionary Guards Corps in Syria and Iraq, but never mind.)
Ramadan has ended. So for Iran, retaliation may be now
or never.
The consensus has been that Iran would bomb an Israeli
embassy in a moral symmetry that might please the Iranian public. Iranian officials have said that no Israeli
embassy was safe from their fury. But another possibility is a direct attack on
Israel, relying heavily on the 155,000 missiles of an Iranian client, the
terrorist group Hezbollah in Lebanon.
This option may seem improbable, because the highly
accurate Iron Dome defense system shields Israeli cities from drones and
ballistic missiles. Well, let us accept the claim of its co-producer that
the Dome can intercept (that is,
destroy) an incoming projectile with 90% accuracy. (The producer is Rafael
Defense Systems of Israel, which produced the Dome with Raytheon of the United
States.) Suppose that Hezbollah and other Iranian clients launch a flock of 30
missiles at Israel. Given the size of the Hezbollah arsenal, an expenditure of
30 missiles looks like a modest investment in violence. Then a simple
calculation suggests a 16% probability, or about one chance in seven, that at
least five missiles will survive the Dome. That would be enough for Iran to
make its point. The calculations are
below. -- Leon Taylor, Seymour, Indiana, tayloralmaty@gmail.com
Notes
For useful comments, I thank but do not implicate Dmitriy Belyanin, Annabel Benson, and Mark Kennet.
I assume that the probability that the Dome will destroy an incoming missile is 90% and is independent of its interception of any other of 30 missiles. (By “independence,” I mean that the Dome’s response to one missile does not affect its response to any other.) This scenario fits the Bernoulli probability distribution. The probability that the Dome would fail to intercept at least 5 of 30 missiles is
Sum [i = 5 to 30] ( 30! / (i! (30 – i)!))* (.1)^i *(.9)^(30
– i) .
I calculate that this is just under 16%.
References
Times of Israel.
Iron Dome is facing its greatest test in war with Hamas. https://www.timesofisrael.com/iron-dome-is-facing-its-greatest-test-in-war-with-hamas/#:~:text=How%20accurate%20is%20the%20Iron,%25%20effective%2C%20according%20to%20Rafael.&text=But%20it%20can%20get%20overwhelmed,allowing%20some%20to%20slip%20through. October 14, 2022.
Cassandra Vinograd.
Iran
Says Israel ‘Will Be Punished’ for Strike in Syria - The New York Times
(nytimes.com) April 10,
2024.
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